16/4x-6/2x=24

Solution for 16/4x-6/2x=24 equation:

16/4x-6/2x=24

We move all terms to the left:

16/4x-6/2x-(24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


32x/8x^2+(-24x)/8x^2-24=0

We multiply all the terms by the denominator


32x+(-24x)-24*8x^2=0

Wy multiply elements

-192x^2+32x+(-24x)=0

We get rid of parentheses

-192x^2+32x-24x=0

We add all the numbers together, and all the variables

-192x^2+8x=0

a = -192; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-192)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-192}=\frac{-16}{-384}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-192}=\frac{0}{-384}
=0
$